Density of circles centered on like circumference

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The discussion revolves around constructing circles of equal radius centered on the circumference of an initial circle and deriving a probability density for the distribution of points from these resultant circles. It is suggested that every point, except for the center, would be covered by at least two overlapping circles. This overlapping leads to a potential uniform distribution of points across the area. The conversation explores the mathematical implications of this setup, particularly in terms of probability density. The inquiry emphasizes understanding the geometric relationships and their effects on point distribution.
Loren Booda
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Imagine a circle of given radius. Construct all circles of equivalent radii whose centers constitute that initial circumference. Can you derive a probability density that describes the overall distribution of points from those resultant circles?
 
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Unless I'm misinterpreting you, I would think that every point covered by these many circles except for the center point would have been overlapped exactly twice.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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